Question

How do you find all solutions in the interval [0,2pi) of the equation `cos x = cot x`?

Answer 1

`0, pi/2, (3pi)/2, 2pi`

Explanation:

f(x) = cos x - cot x = 0
`cos x - cos x/sin x = 0`
`cos^2 x - cos x = 0` (condition: sin x different to zero)
`cos x( cos x - 1) = 0`
a. cos x = 0 --> `x = pi/2 and x = (3pi)/2`
b. cos x = 1 --> x = 0 and `x = 2pi`
Answer for `(0, 2pi):`
`0, pi/2, (3pi)/2, 2pi`